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Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{7}   &  1.0 & +  7.00 x_{1} & +  5.00 x_{2} & -10.00 x_{3} & +  5.00 x_{4} & -4.00 x_{5} & -4.00 x_{6}\\
 x_{8}   &  1.0 & -3.00 x_{1} & +  3.00 x_{2} & +  9.00 x_{3} & + 10.00 x_{4} &   & -4.00 x_{6}\\
 x_{9}   &  -1.0 & +  6.00 x_{1} & -5.00 x_{2} & -7.00 x_{3} & +  2.00 x_{4} & +  1.00 x_{5} &   \\
 x_{10}   &  -2.0 & -4.00 x_{1} & -8.00 x_{2} & -2.00 x_{3} & +  5.00 x_{4} & +  5.00 x_{5} & +  7.00 x_{6}\\
 x_{11}   &  -1.0 & -2.00 x_{1} & +  7.00 x_{2} & -3.00 x_{3} & -2.00 x_{4} & -7.00 x_{5} & -3.00 x_{6}\\
 x_{12}   &  -1.0 & -2.00 x_{1} & -5.00 x_{2} & -6.00 x_{3} & -1.00 x_{4} & +  3.00 x_{5} & +  3.00 x_{6}\\
 x_{13}   &  0.0 & +  2.00 x_{1} & +  3.00 x_{2} & -9.00 x_{3} & -7.00 x_{4} & -5.00 x_{5} & +  7.00 x_{6}\\
 x_{14}   &  -3.0 & -8.00 x_{1} & + 10.00 x_{2} &   & +  2.00 x_{4} & -2.00 x_{5} & + 10.00 x_{6}\\
\hline
z    &  0.0 & +  2.00 x_{1} & -3.00 x_{2} &   & -3.00 x_{4} & +  4.00 x_{5} & +  4.00 x_{6}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{6}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,14$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -7.00 y_{7} & +  3.00 y_{8} & -6.00 y_{9} & +  4.00 y_{10} & +  2.00 y_{11} & +  2.00 y_{12} & -2.00 y_{13} & +  8.00 y_{14}\\
 y_{2}   &  1.0 & -5.00 y_{7} & -3.00 y_{8} & +  5.00 y_{9} & +  8.00 y_{10} & -7.00 y_{11} & +  5.00 y_{12} & -3.00 y_{13} & -10.00 y_{14}\\
 y_{3}   &  1.0 & + 10.00 y_{7} & -9.00 y_{8} & +  7.00 y_{9} & +  2.00 y_{10} & +  3.00 y_{11} & +  6.00 y_{12} & +  9.00 y_{13} &   \\
 y_{4}   &  1.0 & -5.00 y_{7} & -10.00 y_{8} & -2.00 y_{9} & -5.00 y_{10} & +  2.00 y_{11} & +  1.00 y_{12} & +  7.00 y_{13} & -2.00 y_{14}\\
 y_{5}   &  1.0 & +  4.00 y_{7} &   & -1.00 y_{9} & -5.00 y_{10} & +  7.00 y_{11} & -3.00 y_{12} & +  5.00 y_{13} & +  2.00 y_{14}\\
 y_{6}   &  1.0 & +  4.00 y_{7} & +  4.00 y_{8} &   & -7.00 y_{10} & +  3.00 y_{11} & -3.00 y_{12} & -7.00 y_{13} & -10.00 y_{14}\\
\hline
z    &  -0 & -1.00 y_{7} & -1.00 y_{8} & +  1.00 y_{9} & +  2.00 y_{10} & +  1.00 y_{11} & +  1.00 y_{12} &   & +  3.00 y_{14}\\
\end{array}\]
Unbounded Dictionary!
Initialization returns unbounded dual dictionary after 4 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{9}   &  0.723214285714 & -3.96 y_{7} & -3.90 y_{8} & -0.17 y_{1} & -0.39 y_{4} & -0.16 y_{2} & +  1.54 y_{12} & +  1.93 y_{13} & -1.04 y_{14}\\
 y_{11}   &  1.02678571429 & -5.29 y_{7} & -6.85 y_{8} & -0.08 y_{1} & -0.61 y_{4} & -0.34 y_{2} & +  2.46 y_{12} & +  3.07 y_{13} & -3.96 y_{14}\\
 y_{3}   &  9.78571428571 & -36.64 y_{7} & -63.21 y_{8} & -1.36 y_{1} & -5.14 y_{4} & -2.29 y_{2} & + 25.29 y_{12} & + 35.43 y_{13} & -22.29 y_{14}\\
 y_{10}   &  0.321428571429 & -1.54 y_{7} & -3.18 y_{8} & +  0.04 y_{1} & -0.29 y_{4} & -0.07 y_{2} & +  0.57 y_{12} & +  1.86 y_{13} & -1.57 y_{14}\\
 y_{5}   &  5.85714285714 & -21.43 y_{7} & -28.14 y_{8} & -0.57 y_{1} & -2.43 y_{4} & -1.86 y_{2} & +  9.86 y_{12} & + 15.29 y_{13} & -16.86 y_{14}\\
 y_{6}   &  1.83035714286 & -1.13 y_{7} & +  5.71 y_{8} & -0.49 y_{1} & +  0.18 y_{4} & -0.52 y_{2} & +  0.39 y_{12} & -10.79 y_{13} & -10.89 y_{14}\\
\hline
z    &  2.39285714286 & -13.32 y_{7} & -18.11 y_{8} & -0.18 y_{1} & -1.57 y_{4} & -0.64 y_{2} & +  6.14 y_{12} & +  8.71 y_{13} & -5.14 y_{14}\\
\end{array}\]
Original Problem is Infeasible
Infeasible Problem.. Early Exit
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